In the present work we are interested in the ST of systems exhibiting
anomalous diffusion, where \(\langle x^2(t)\rangle \propto t^{\alpha }\)  with \(\alpha \ne 1\) . Here, the case \(\alpha <1\)  is
referred to as subdiffusion, while \(\alpha >1\)  corresponds to
superdiffusion [1]}, [2]}, [3]}.
Anomalous dynamics occurs in a large variety of systems (see, e.g.,
Refs. [4]}, [2]}, [6]}, [7]}). Typically,
subdiffusion is related to crowding phenomena (where the motion is
hindered by obstacles) or spatial confinement 
[8]}, [7]}, [10]}. In turn, superdiffusion
occurs, e.g., in glassy material [11]}, for cell
migration [12]}, [13]}, and in the foraging of biological
organisms [6]}. From a theoretical point of view, various
types of models have been proposed to describe anomalous dynamics
[15]}. One class of these models is Markovian in
character, where the future of the observable, e.g., \(x\) , only
depends on the current value. Examples of (semi-)Markovian
models yielding anomalous diffusion include continuous time random
walks
[16]}, [17]}, heterogeneous diffusion
processes [18]}, anomalous diffusion in
disordered media [19]}, [20]}
and scaled Brownian motion [21]}, [22]}. But there are
furthermore many non-Markovian models predicting anomalous
diffusion. Prominent examples are the generalized Langevin
equation (GLE) with friction ("memory") kernel and colored
noise [23]}, [24]}, as well as
fractional Brownian motion (FBM) [25]}, [26]}, where memory arises through the noise
correlation function. The FBM process, which has been widely observed
in experiments (see, e.g., Ref. [27]} for references),
is of particular interest in the present work.
